Question 327: Waves

Question

A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the ratio

Accepted Answer

First overtone for open pipe, $$V_{01}=\frac{2 \mathrm{v}}{2 I_0}$$
First overtone for close pipe, $$V_{C 1}=\frac{3 V}{4 I_C}$$
According to question, $$V_{01}=V_{C 1}$$
$$\begin{array}{ll}
\Rightarrow & \frac{2 \mathrm{~V}}{2 I_0}=\frac{3}{4} \frac{\mathrm{V}}{I_C} \
\Rightarrow & \frac{I_C}{I_0}=\frac{3}{4}
\end{array}$$

Answer

$$1: 2$$

Answer

$$2: 3$$

Answer

$$3: 4$$

Answer

$$4: 5$$

Waves

A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the ratio

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